I put the 20" rims that were on my '02 4x2 Silverado on my '05 Avalanche. The rims are rated at 2400# and I think the tires are rated about 2600 (285-50/20). Considering the truck weighs 5500 and an ideal class III towing limit is 5000# [500# tongue wt], that still only get me into the 6000# gross range. so don't think it is much of an issue. With the 5.3L and the 4.10 gears, my truck is rated for a 10,000# (might even be 11,000#) trailer. THat would still only place 1000# on the tongue, but just about any truck would need a weight distributing hitch for stability at that point. If you go with 18" rims, you are most likely into a 285-60/18 to get to the 31.5" ht range of a stock tire. In my case, I ended up smaller diameter from the stock 31.6" to 31.2" (no big deal , 1-1/2% effective increase in gear ratio).
PS - make sure to check the wheels, the rating is cast into the back of all alum wheels. I had first looked at some nice looking, but less costly rims, ended up, they were only rated to 1750#, glad I caught that. Wheels I have now are KO, much better quality.